The paper presents a robust algorithm, which allows to implicitly describe and track immersed geometries within a background mesh. The background mesh is assumed to be unstructured and discretized by tetrahedrons. The contained geometry is assumed to be given as triangulated surface. Within the background mesh, the immersed geometry is described implicitly using a discontinuous distance function based on a level-set approach. This distance function allows to consider both, “double-sided” geometries like membrane or shell structures, and “single-sided” objects for which an enclosed volume is univocally defined. For the second case, the discontinuous distance function is complemented by a continuous signed distance function, whereas ray casting is applied to identify the closed volume regions. Furthermore, adaptive mesh refinement is employed to provide the necessary resolution of the background mesh. The proposed algorithm can handle arbitrarily complicated geometries, possibly containing modeling errors (i.e., gaps, overlaps or a non-unique orientation of surface normals). Another important advantage of the algorithm is the embarrassingly parallel nature of its operations. This characteristic allows for a straightforward parallelization using MPI. All developments were implemented within the open source framework “KratosMultiphysics” and are available under the BSD license. The capabilities of the implementation are demonstrated with various application examples involving practice-oriented geometries. The results finally show, that the algorithm is able to describe most complicated geometries within a background mesh, whereas the approximation quality may be directly controlled by mesh refinement.

中文翻译：

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一种可靠的算法，用于隐式描述背景网格中的浸入式几何

本文提出了一种鲁棒的算法，该算法可以隐式描述和跟踪背景网格内的沉浸几何。假定背景网格是无结构的且由四面体离散。假定所包含的几何形状为三角表面。在背景网格内，使用基于级别集方法的不连续距离函数隐式描述沉浸的几何体。该距离函数允许同时考虑“双面”几何形状（如膜或壳结构）和“单面”对象，为其唯一定义了封闭体积。对于第二种情况，不连续距离函数由连续的有符号距离函数补充，而射线投射用于识别封闭的体积区域。此外，自适应网格细化用于提供背景网格的必要分辨率。所提出的算法可以处理任意复杂的几何形状，可能包含建模误差（即，表面法线的间隙，重叠或非唯一方向）。该算法的另一个重要优点是其操作具有令人尴尬的并行性。此特性允许使用MPI进行直接并行化。所有开发都在开源框架“ KratosMultiphysics”中实现，并已获得BSD许可。通过涉及面向实践的几何的各种应用示例来演示实现的功能。结果最终表明，该算法能够描述背景网格中最复杂的几何形状，